July 2012 - mathfun@mailman.xmission.com

[math-fun] quaternion identity
by rcs＠xmission.com 19 Jul '12

19 Jul '12

Has anyone seen this somewhere? Quaternions a,b,c,d: abcd+acdb+adbc+badc+bcad+bdca+cabd+cbda+cdab+dacb+dbac+dcba = abdc+acbd+adcb+bacd+bcda+bdac+cadb+cbad+cdba+dabc+dbca+dcab The LHS is even permutations of abcd; RHS is odd. It should also work for 2x2 matrices of real or complex numbers. Rich

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[math-fun] fibonacci megamillions
by Thane Plambeck 18 Jul '12

18 Jul '12

if you'd chosen to play 5 random fibonacci numbers in the appropriate range [1,56] you would have had a positive expected return in yesterday's megamillions lottery drawing the 49 and 17 (the mega number) spoiled it a bit, but still. and clearly 17 was the mega because it was july 17th, and 49 is 7^2. http://www.megamillions.com/numbers/drawDetails.asp?drawDate=7/17/2012 -- Thane Plambeck tplambeck(a)gmail.com http://counterwave.com/

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[math-fun] what is known about the squareful Fibonacci numbers?
by Wouter Meeussen 16 Jul '12

16 Jul '12

[[ apart from the fact that any fib(n) containing a factor p^i (i>1 of course) seems to have mod(n,p)=0 ]] up to fib(258), at least one of fib(k) .. fib(k+6) is squareful. Analogously, the squareful fibs are spaced no more than 6 apart. Anyone for a counter-example? Their separations are counted as {1, 5 times}, {2, 11 times}, {3, 5}, {4, 7}, {5, 4}, {6, 27} So 6 is a ‘preferred distance’ for lowish n. Wouter

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[math-fun] Polynomial puzzle I heard today
by Mike Stay 15 Jul '12

15 Jul '12

Is there a multivariate polynomial whose image over R^n is strictly positive? -- Mike Stay - metaweta(a)gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com

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[math-fun] Someone finally reports on what Shouryya Ray actually did
by Mike Stay 14 Jul '12

14 Jul '12

http://goo.gl/jh6Pr -- Mike Stay - metaweta(a)gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com

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Re: [math-fun] Tree terminology
by Christian G. Bower 13 Jul '12

13 Jul '12

Tree terminology is far from standardized as many texts use the same terms inconsistently, but I can share what I have become accustomed to. I tend to use "tree" related to graph-theory terms, thus we have: tree: connected graph with no closed cycles. rooted tree: tree with a distinguished node called the root. Thus the "trees" you're referring to are actually rooted trees. Note that: o o | /|\ o and o o o / \ o o are the same tree but different rooted trees. Rooted trees correspond to the hierarchies used in data structures and other applications. Rooted tree is the name of the "X" in your question. We are often interested in applying some sort of combinatorial arrangement to the children of a node. A book I've referenced a lot on the subject _Combinatorial Species and Tree-Like Structures_ by Bergeron, Labelle and Leroux uses the term R-enriched rooted tree for such a structure where R represents some combinatorial structure. If R is a set we have rooted tree or what you're calling "X" If R is linear order we have ordered rooted tree or what you're calling "tree" If R is cycle we have mobile. ------ Original Message ------ Received: Wed, 11 Jul 2012 10:44:21 PM PDT From: Marc LeBrun <mlb(a)well.com> To: math-fun <math-fun(a)mailman.xmission.com> Subject: [math-fun] Tree terminology > Speaking of terminology, I¹m drawing a blank: > > Tree is to Composition > AS > X is to Partition > > X == ...? > > For example the following are distinct Trees, but equivalent X¹s: > > O O > / \ / \ > O O O O > / \ \ / / \ > O O O O O O > > Thanks! > --MLB > > > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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[math-fun] Tree terminology
by Marc LeBrun 12 Jul '12

12 Jul '12

Speaking of terminology, I¹m drawing a blank: Tree is to Composition AS X is to Partition X == ...? For example the following are distinct Trees, but equivalent X¹s: O O / \ / \ O O O O / \ \ / / \ O O O O O O Thanks! --MLB

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Re: [math-fun] Polynomial puzzle I heard today
by Dan Asimov 10 Jul '12

10 Jul '12

If n = 1, then Andy's extension of P: R^n -> R to the one-point compactifications P*: (R^n)* -> R* would indeed be continuous. But for n >= 2, this is not necessarily the case, since (say n=2) it may not be true that |P(x,y)| -> oo as |(x,y)| -> oo. E.g., P(x,y) := xy. --Dan Andy wrote: << On Mon, Jul 9, 2012 at 9:52 PM, Mike Stay <metaweta(a)gmail.com> wrote: > On Mon, Jul 9, 2012 at 6:51 PM, Mike Stay <metaweta(a)gmail.com> wrote: >> On Mon, Jul 9, 2012 at 6:50 PM, Mike Stay <metaweta(a)gmail.com> wrote: >>> Is there a multivariate polynomial whose image over R^n is strictly positive? >> >> Sorry, "strictly the positive reals". > > Or better: "exactly the strictly positive reals." No. Add a point at infinity to R^n and to R, extend the multvariate polynomial by mapping the point at infinity to the point at infinity, and the resulting function is still compact. Since the range is compact, so is the image. So the image of the original polynomial is compact once the point at infinity is added, and so it cannot e the strictly positive reals, since infinity maps to infinity, not 0. >> ________________________________________________________________________________________ It goes without saying that .

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Re: [math-fun] inverter down?
by Simon Plouffe 10 Jul '12

10 Jul '12

Hello, no I do not maintain it anymore, there are several reasons, the data is from 1999, it is outdated in many areas. the size of the current one is 751 gb or 5.848 billion entries this is way too big for the disks at uqam. I increased the size of each entry to 64 digits, it means that for any computation, the growth rate is exponential, in plain english, it takes too much cpu to be left on the internet, some tests takes 1 minute to run. I tried a launch in 2011 at my site : http://www.plouffe.fr/ well, with 1.4 tb of data, the only client I had was google bots and some requests, at a cost of about 80 dollars per month. I decided to pull the plug and answer individual requests one by one : So, if you have 1 request or a series of numbers, just send them in I can take 20 meg of data on gmail , I would be glad to answer any of them, best regards, simon plouffe Le 10/07/2012 05:34, Mike Stay a Ã©crit : > I haven't been able to get the inverter to let me browse for about a > week. Do you still manage that?

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[math-fun] this could be of interest : Announcing the LMFDB
by Simon Plouffe 10 Jul '12

10 Jul '12

Hello, there is a lot of material on that site, very neat, best regards and bonne journÃ©e, simon plouffe -------- Message original -------- Sujet: Announcing the LMFDB Date : Mon, 9 Jul 2012 21:51:38 -0500 De : LMFDB <lmfdb(a)lmfdb.org> RÃ©pondre Ã : Number Theory List <NMBRTHRY(a)LISTSERV.NODAK.EDU>, LMFDB <lmfdb(a)lmfdb.org> Pour : NMBRTHRY(a)LISTSERV.NODAK.EDU We are pleased to announce the release of the LMFDB: the L-functions and Modular Forms Database. http://www.lmfdb.org The LMFDB seeks to be a modern handbook for objects of research in number theory and related areas. It provides formulas, tables, graphs, and data, with an emphasis on exhibiting concrete examples and illustrating the connections between related objects. Browse and search pages provide easy access for both experts and non-experts. Every object has its own 'homepage,' which has a permanent and mathematically meaningful URL. In this initial release, the LMFDB has well-developed material for: Dirichlet characters and Dirichlet L-functions Elliptic curves/Q and their L-functions Holomorphic cusp forms on GL(2)/Q and their L-functions Number fields, both local and global, their Galois groups, and Dedekind zeta functions In addition, there is material available under various stages of development for: Maass forms on GL(2)/Q and their L-functions Hilbert modular forms and their L-functions Siegel modular forms and their L-functions L-functions of Maass forms on GL(3), GL(4), and Sp(4) Artin representations and Artin L-functions Symmetric power L-functions The LMFDB seeks to be an ongoing and growing resource for the research mathematics community. We welcome feedback via the feedback form available on the website: http://www.lmfdb.org The project is open source, with the code available at http://code.google.com/p/lmfdb/ Regards, The LMFDB collaboration Managing Editors: Jonathan Bober, Andrew Booker, Brian Conrey, John Cremona, David Farmer, Ralph Furmaniak, John Jones, Kiran S. Kedlaya, Michael Rubinstein, Harald Schilly, Ralf Schmidt, William Stein, Holly Swisher Editors: Jonathan Bober, Paul-Olivier Dehaye, John Cremona, John Jones, Stefan Lemurell, Pascal Molin, Nathan Ryan, Nils-Peter Skoruppa, Fredrik StrÃ¶mberg, John Voight LMFDB Contributors: Matthew Alderson, Salman Baig, Jennifer Balakrishnan, Jennifer Beineke, Jonathan W. Bober, Andrew Booker, Robert Bradshaw, Alina Bucur, Henri Cohen, Brian Conrey, John Cremona, Paul-Olivier Dehaye, Lassina Dembele, Tim Dokchitser, Stephan Ehlen, David W. Farmer, Marcus Fraczek, Ralph Furmaniak, Jonathan Hanke, William Hart, Ghaith Hiary, Duc Khiem Huynh, John Jones, Jon Keating, Kiran S. Kedlaya, Kamal Khuri-Makdisi, Sally Koutsoliotas, Stefan Lemurell, Robert Miller, Pascal Molin, David Platt, Cris Poor, Rishikesh, David Roberts, David Roe, Michael Rubinstein, Nathan Ryan, Ralf Schmidt, Harald Schilly, Gagan Sekhon, Nils-Peter Skoruppa, William Stein, Fredrik Stroemberg, Holly Swisher, Gonzalo Tornaria Holger Then, John Voight, Lynne Walling, Mark Watkins, Jamie Weigandt, Trevor Wooley, David Yuen

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